Question

Упростите выражение.
(5/25-х^2 + 1/х-5) : х/2х^2-20х+50

Answer 1

$1)\frac{5}{25-x^{2} } +\frac{1}{x-5}=\frac{5}{(5-x)(5+x)}-\frac{1}{5-x}=\frac{5-5-x}{(5-x)(5+x)}=-\frac{x}{(5-x)(5+x)}=\frac{x}{(x-5)(x+5)}\\\\2)\frac{x}{(x-5)(x+5)}:\frac{x}{2x^{2}-20x+50 }=\frac{x}{(x-5)(x+5)}*\frac{2(x^{2}-10x+25) }{x}= \frac{2(x-5)^{2} }{(x-5)(x+5)}=\frac{2x-10}{x+5}$